Grace Cacciola was promoted to Emergency Medical Service deputy chief in 2014 after she helped write her own glowing evaluation and a superior officer “inappropriately directed” an underling to sign it, documents allege.

In a Jan. 17 notarized statement obtained by The Post, EMS Deputy Chief Martin Braun says then-Staten Island Commander Janice Olszewski told him to sign Cacciola’s 2013 annual performance evaluation as if he was the author.

“I was not afforded an opportunity to review this document prior to signing as author, nor was I afforded any opportunity to contribute to its findings,” Braun states.

“Although my actions may be construed as inappropriate, I was under duress on this occasion as Chief Olszewski was my immediate supervisor and was responsible for writing my own personal evaluations.”

In a separate e-mail to the FDNY’s inspector general, Braun said Olszewski “coerced me” into signing Cacciola’s evaluation. Olszewski “later became one of the top leaders in the FDNY EMS chain of command, a situation that further prevented me from coming forward.”

Braun declined to comment on his statements.

Last year, Olszewski retired. Cacciola was then promoted to division chief, but works at FDNY headquarters as chief of “planning and strategy,” which prepares for events such as the NYC Marathon. Her salary rose to $132,054.

Braun gave the notarized statement to lawyer Yetta Kurland, who is representing paramedics and EMTs in a federal lawsuit against the FDNY’s “subjective promotional process.”

The suit charges the system has denied opportunities to women and minorities who are qualified for promotion.

While unfamiliar with the facts in Cacciola’s case, Kurland said, “Anybody who cheats in the promotional process obviously should not be appointed. To the extent that people are able to circumvent the process or misuse it, that’s all the more reason why we want to put in place a standardized, civil-service exam.”

One insider put it bluntly: “It’s all favoritism — it’s who you know.”

While firefighters can earn promotion to five higher ranks based on civil-service exams, the city has only one promotional exam in EMS — from paramedic to lieutenant. All those trying to rise above lieutenant must be appointed by the brass.

A recently enacted law will add EMS promotional exams.

Asked about the allegation, Cacciola said, “I don’t know where that came from.”

Olszewski “sat in front of me and issued it to me,” she said of her 2014 evaluation.

Asked who wrote it, Cacciola said, “I am not having this conversation with you,” and hung up. Olszewski, who moved to Florida, could not be reached.

Previously, Cacciola was caught in a cheating scandal at the EMS Academy in 2002, when participants were given passing scores on a state-required practical skills refresher test without taking it. A deputy chief and Cacciola, then a lieutenant, were suspended.

Cacciola “was disciplined following the investigation and hearing,” said FDNY spokesman James Long, declining to elaborate.

On the alleged sham evaluation, Long said, “The Department will look into the claim.”